Mutual Inductance Calculation Method of Arbitrarily Positioned Circular Coils with Convex Ring Type Finite Magnetic Shielding in Wireless Power Transfer
Lin Zhiyuan1, Li Zhongqi1,2, Hu Changxuan1, Chen Zhongbang1, Huang Shoudao2
1. College of Railway Transportation Hunan University of Technology Zhuzhou 412007 China; 2. College of Electrical and Information Engineering Hunan University Changsha 410082 China
Abstract In practice, the structure of the wireless power transfer (WPT) system varies for different application scenarios. And the relative position change between the coils of the transmission system will also be caused by the change of mutual inductance. This affects the transmission efficiency. How to quickly and accurately calculated the mutual inductance is a key step in the process of designing and optimizing the structure of WPT systems. Therefore, it is important to study the calculation method of mutual inductance of coils in WPT system under different relative positions. There is no method for mutual inductance calculation of arbitrary positioned circular coils with convex ring type finite magnetic shielding. This paper established the model for mutual inductance calculation of circular coil with convex ring type finite magnetic shielding in arbitrary position. The spatial boundary vector analysis method is proposed for the exact solution of mutual inductance. This method is solved for the magnetic vector potential in each region by boundary conditions. The space vector coordinate transformation method is utilized. The expression for the calculation of mutual inductance in arbitrary position is obtained by combining Neumann's formula. The validity of the proposed formula is verified by simulations and experiments from four variations of coil relative position vertical offset, horizontal offset, horizontal angular deflection and horizontal offset plus angular deflection. The calculated results of the proposed formula are compared with the simulated and experimental results as follows: (1) The maximum error of the calculated results with the simulated and experimental results for vertical offset are 2.84% and 2.48%, respectively. (2) The maximum error of the calculated results with the simulated and experimental results for horizontal offset are 1.49% and 2.85%, respectively. (3) The maximum error of the calculated results with the simulated and experimental results for horizontal angular deflection are 3.26% and 2.86%, respectively. 4) The maximum error of the calculated results with the simulated and experimental results for horizontal offset plus angular deflection are 1.84% and 2.47%, respectively. The calculation model is written Matlab as a program and Ansys Maxwell simulation software under the same equipment for speed comparison. The shortest average time for Ansys Maxwell simulation is 105.636 s, while the longest average time for Matlab program is 0.121 s. Therefore, the proposed calculation method has a significant advantage in calculation speed. The model structure saved 19.6% material compared to the traditional disk type structure under the same parameters. Except for high angle deflection, the mutual inductance can reach 99% of the mutual inductance of the disk type. In conclusion, the calculated, simulated and experimental values of mutual inductance are in good agreement. The correctness of the proposed calculation method is verified.
Lin Zhiyuan,Li Zhongqi,Hu Changxuan等. Mutual Inductance Calculation Method of Arbitrarily Positioned Circular Coils with Convex Ring Type Finite Magnetic Shielding in Wireless Power Transfer[J]. Transactions of China Electrotechnical Society, 2024, 39(16): 4918-4930.
[1] 周玮, 蓝嘉豪, 麦瑞坤, 等. 无线充电电动汽车V2G模式下光储直流微电网能量管理策略[J]. 电工技术学报, 2022, 37(1): 82-91. Zhou Wei, Lan Jiahao, Mai Ruikun, et al.Research on power management strategy of DC microgrid with photovoltaic, energy storage and EV-wireless power transfer in V2G mode[J]. Transactions of China Electrotechnical Society, 2022, 37(1): 82-91. [2] 孙淑彬, 张波, 李建国, 等. 多负载磁耦合无线电能传输系统的拓扑发展和分析[J]. 电工技术学报, 2022, 37(8): 1885-1903. Sun Shubin, Zhang Bo, Li Jianguo, et al.Analysis and development on topologies of multi-load magnetic-coupling wireless power transfer system[J]. Transactions of China Electrotechnical Society, 2022, 37(8): 1885-1903. [3] 冯天旭, 史可, 孙跃, 等. 基于互感识别及移相角优化的全方位无线电能传输系统靶向传能方法[J]. 电工技术学报, 2023, 38(24): 6581-6595. Feng Tianxu, Shi Ke, Sun Yue, et al.Targeted power transfer method for omnidirectional wireless power transfer system based on mutual inductance identification and phase-shift angle optimization[J]. Transactions of China Electrotechnical Society, 2023, 38(24): 6581-6595 [4] 苏玉刚, 钱林俊, 刘哲, 等. 水下具有旋转耦合机构的电场耦合无线电能传输系统及参数优化方法[J]. 电工技术学报, 2022, 37(10): 2399-2410. Su Yugang, Qian Linjun, Liu Zhe, et al.Underwater electric-filed coupled wireless power transfer system with rotary coupler and parameter optimization method[J]. Transactions of China Electrotechnical Society, 2022, 37(10): 2399-2410. [5] 陈凯楠, 蒋烨, 檀添, 等. 轨道交通350 kW大功率无线电能传输系统研究[J]. 电工技术学报, 2022, 37(10): 2411-2421, 2445. Chen Kainan, Jiang Ye, Tan Tian, et al.Research on 350 kW high power wireless power transfer system for rail transit[J]. Transactions of China Electrotechnical Society, 2022, 37(10): 2411-2421, 2445. [6] 陈永洪, 黎祎阳, 杨斌, 等. 基于多中继线圈结构的无线电能传输系统恒流/恒压输出方法[J]. 电力系统自动化, 2022, 46(20): 147-154. Chen Yonghong, Li Yiyang, Yang Bin, et al.Constant-current/constant-voltage output method for wireless power transfer system based on multi-relay coil structure[J]. Automation of Electric Power Systems, 2022, 46(20):147-154. [7] Xu Yanhui, Gao Yihao, Cheng Yundan, et al.Substation clustering based on improved KFCM algorithm with adaptive optimal clustering number selection[J]. Global Energy Interconnection, 2023, 6(4): 505-516. [8] Wu Dehui, Huang Chao, Yang Fan, et al.Analytical calculations of self‐and mutual inductances for rectangular coils with lateral misalignment in IPT[J]. IET Power Electronics, 2019, 12(15): 4054-4062. [9] Babic S, Akyel C.Improvement in calculation of the self-and mutual inductance of thin-wall solenoids and disk coils[J]. IEEE Transactions on Magnetics, 2000, 36(4): 1970-1975. [10] Lü Yuelong, Meng Fanyi, Yang Gaohui, et al.A method of using nonidentical resonant coils for frequency splitting elimination in wireless power transfer[J]. IEEE Transactions on Power Electronics, 2015, 30(11): 6097-6107. [11] Conway J T.Inductance calculations for noncoaxial coils using bessel functions[J]. IEEE Transactions on Magnetics, 2007, 43(3): 1023-1034. [12] 李中启, 李晶, 全倡辉, 等. 无线电能传输系统带磁屏蔽任意位置矩形线圈的互感计算[J]. 电工技术学报, 2022, 37(17): 4294-4305. Li Zhongqi, Li Jing, Quan Changhui, et al.Mutual inductance calculation of arbitrarily positioned rectangular coils with magnetic shielding in wireless power transfer systems[J]. Transactions of China Electrotechnical Society, 2022, 37(17): 4294-4305. [13] Liu Fuxin, Yang Yong, Jiang Dan, et al.Modeling and optimization of magnetically coupled resonant wireless power transfer system with varying spatial scales[J]. IEEE Transactions on Power Electronics, 2016, 32(4): 3240-3250. [14] Tavakkoli H, Abbaspour-Sani E, Khalilzadegan A, et al.Mutual inductance calculation between two coaxial planar spiral coils with an arbitrary number of sides[J]. Microelectronics Journal, 2019, 85: 98-108. [15] Choi Hyojin, Lee Sangbin, Cha Cheolung.Optimization of geometric parameters for circular loop antenna in magnetic coupled wireless power transfer[C]//2014 IEEE Wireless Power Transfer Conference, Jeju, Korea (South), 2014: 280-283. [16] Pirinççi N, Altun H.A new analytical study on mutual inductance calculations for wireless power transfer using magnetic vector potential[J]. IEEE Transactions on Magnetics, 2022, 58(8): 1-14. [17] Song Kaihong, Feng Jian, Zhao Ran, et al.A general mutual inductance formula for parallel non-coaxial circular coils[J]. The Applied Computational Electromagnetics Society Journal (ACES), 2019: 1385-1390. [18] Wang Yiming, Xie Xu, Zhou Yan, et al.Calculation and modeling analysis of mutual inductance between coreless circular coils with rectangular cross section in arbitrary spatial position[C]//2020 IEEE 5th Information Technology and Mechatronics Engineering Conference (ITOEC), Chongqing, China, 2020: 1258-1267. [19] Zhang Xian, Meng Hao, Wei Bin, et al.Mutual inductance calculation for coils with misalignment in wireless power transfer[J]. The Journal of Engineering, 2019, 2019(16): 1041-1044. [20] Liu Shuo, Su Jianhui, Lai Jidong, et al.Precise modeling of mutual inductance for planar spiral coils in wireless power transfer and its application[J]. IEEE Transactions on Power Electronics, 2021, 36(9): 9876-9885. [21] Liu Shuo, Su Jianhui, Lai Jidong.Accurate expressions of mutual inductance and their calculation of archimedean spiral coils[J]. Energies, 2019, 12(10): 2017. [22] Luo Zhichao, Wei Xuezhe.Mutual inductance analysis of planar coils with misalignment for wireless power transfer systems in electric vehicle[C]//2016 IEEE Vehicle Power and Propulsion Conference (VPPC), Hangzhou, China, 2016: 1-6. [23] Han Yang, Wang Xiaoming.Calculation of mutual inductance based on field-circuit coupling analysis for WPT[C]//2013 5th International Conference on Power Electronics Systems and Applications (PESA), Hong Kong, China, 2013: 1-5. [24] Luo Zhichao, Wei Xuezhe.Analysis of square and circular planar spiral coils in wireless power transfer system for electric vehicles[J]. IEEE Transactions on Industrial Electronics, 2017, 65(1): 331-341. [25] Dong Zifan, Li Xiaoming, Liu Sheng, et al.A novel all-direction antimisalignment wireless power transfer system designed by truncated region eigenfunction expansion method[J]. IEEE Transactions on Power Electronics, 2021, 36(11): 12456-12467. [26] Zhang Xueyi, Quan Changhui, Li Zhongqi.Mutual inductance calculation of circular coils for an arbitrary position with electromagnetic shielding in wireless power transfer systems[J]. IEEE Transactions on Transportation Electrification, 2021, 7(3): 1196-1204. [27] 李中启, 林志远, 杨鹏, 等. 无线电能传输系统带双层有界磁屏蔽任意位置圆形线圈的耦合系数计算[J]. 电工技术学报, 2022, 37(24): 6306-6318. Li Zhongqi, Lin Zhiyuan, Yang Peng, et al.Calculation of the coupling coefficient of an arbitrarily positioned circular coil for wireless power transfer system with a double-layered finite magnetic shield[J]. Transactions of China Electrotechnical Society, 2022, 37(24): 6306-6318. [28] 李厚基, 王春芳, 魏芝浩, 等. 无线电能传输系统用屏蔽层结构的研究[J]. 电工电能新技术, 2019, 38(5): 74-83. Li Houji, Wang Chunfang, Wei Zhihao, et al.Research of shield structure for wireless power transfer system[J]. Advanced Technology of Electrical Engineering and Energy, 2019, 38(5): 74-83.
2024, Vol. 39 
